Abstract

Paraxial wave equations are derived for the propagation of beams in uniform uniaxial anisotropic media. The equations are generalized to the case of nonuniform media with weakly varying refractive indices. An ordinary wave beam is governed by a standard paraxial equation, whereas an extraordinary wave beam is governed by a paraxial wave equation, which involves both a displacement relative to the position of an ordinary wave beam and a rescaling of one transverse coordinate. The solution to the latter equation for a propagating Gaussian beam displays a distortion of both shape and phase front. Numerical results for diffraction by a uniformly illuminated circular aperture in a calcite medium display various anomalies ascribable to a loss of circular symmetry.

© 1983 Optical Society of America

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  1. See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1970), pp. 665–681.
  2. For a comprehensive treatment of the propagation of Gaussian beams, see, for example, J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976), Chap. 2.
  3. A review of such devices can be found in R. C. Alferness, "Guided-wave devices for optical communication," IEEE J. Quantum Electron. QE-17, 946–991 (1981).
  4. W. K. Burns and J. Warner, "Mode dispersion in uniaxial optical waveguides," J. Opt. Soc. Am. 64, 441–446 (1974).
  5. R. A. Steinberg and T. G. Giallorenzi, "Modal fields of anisotropic channel waveguides," J. Opt. Soc. Am. 67, 523–532 (1977).
  6. D. Marcuse, "Modes of a symmetric slab optical waveguide in birefringent media-Part I: optical axis not in plane of slab," IEEE J. Quantum Electron. QE-14, 736–741 (1978).
  7. M. D. Feit and J. A. Fleck, Jr., "Light propagation in graded index fibers," Appl. Opt. 24, 3990–3998 (1978).
  8. The treatment of the paraxial propagation of high-energy laser beams in the atmosphere and other references can be found in J. A. Fleck, Jr., J. R. Morris, and M. D. Feit, "Time-dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129–160 (1976).
  9. This result could be anticipated from the conventional treatment of birefringence. See, for example, Ref. 1. However, the fact that the offset is automatically incorporated in the paraxial wave equation gives assurance that it is correct.
  10. M. D. Feit and J. A. Fleck, Jr., "Mode properties and dispersion for two optical fiber index profiles by the propagating beam method," Appl. Opt. 19, 3140–3150 (1980).
  11. M. D. Feit and J. A. Fleck, Jr., "Propagating beam theory of optical fiber cross coupling," J. Opt. Soc. Am. 71, 1361–1372 (1981).

1981 (2)

A review of such devices can be found in R. C. Alferness, "Guided-wave devices for optical communication," IEEE J. Quantum Electron. QE-17, 946–991 (1981).

M. D. Feit and J. A. Fleck, Jr., "Propagating beam theory of optical fiber cross coupling," J. Opt. Soc. Am. 71, 1361–1372 (1981).

1980 (1)

1978 (2)

D. Marcuse, "Modes of a symmetric slab optical waveguide in birefringent media-Part I: optical axis not in plane of slab," IEEE J. Quantum Electron. QE-14, 736–741 (1978).

M. D. Feit and J. A. Fleck, Jr., "Light propagation in graded index fibers," Appl. Opt. 24, 3990–3998 (1978).

1977 (1)

1976 (1)

The treatment of the paraxial propagation of high-energy laser beams in the atmosphere and other references can be found in J. A. Fleck, Jr., J. R. Morris, and M. D. Feit, "Time-dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129–160 (1976).

1974 (1)

Alferness, R. C.

A review of such devices can be found in R. C. Alferness, "Guided-wave devices for optical communication," IEEE J. Quantum Electron. QE-17, 946–991 (1981).

Arnaud, J. A.

For a comprehensive treatment of the propagation of Gaussian beams, see, for example, J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976), Chap. 2.

Born, M.

See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1970), pp. 665–681.

Burns, W. K.

Feit, M. D.

M. D. Feit and J. A. Fleck, Jr., "Propagating beam theory of optical fiber cross coupling," J. Opt. Soc. Am. 71, 1361–1372 (1981).

M. D. Feit and J. A. Fleck, Jr., "Mode properties and dispersion for two optical fiber index profiles by the propagating beam method," Appl. Opt. 19, 3140–3150 (1980).

M. D. Feit and J. A. Fleck, Jr., "Light propagation in graded index fibers," Appl. Opt. 24, 3990–3998 (1978).

The treatment of the paraxial propagation of high-energy laser beams in the atmosphere and other references can be found in J. A. Fleck, Jr., J. R. Morris, and M. D. Feit, "Time-dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129–160 (1976).

Fleck, Jr., J. A.

M. D. Feit and J. A. Fleck, Jr., "Propagating beam theory of optical fiber cross coupling," J. Opt. Soc. Am. 71, 1361–1372 (1981).

M. D. Feit and J. A. Fleck, Jr., "Mode properties and dispersion for two optical fiber index profiles by the propagating beam method," Appl. Opt. 19, 3140–3150 (1980).

M. D. Feit and J. A. Fleck, Jr., "Light propagation in graded index fibers," Appl. Opt. 24, 3990–3998 (1978).

The treatment of the paraxial propagation of high-energy laser beams in the atmosphere and other references can be found in J. A. Fleck, Jr., J. R. Morris, and M. D. Feit, "Time-dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129–160 (1976).

Giallorenzi, T. G.

Marcuse, D.

D. Marcuse, "Modes of a symmetric slab optical waveguide in birefringent media-Part I: optical axis not in plane of slab," IEEE J. Quantum Electron. QE-14, 736–741 (1978).

Morris, J. R.

The treatment of the paraxial propagation of high-energy laser beams in the atmosphere and other references can be found in J. A. Fleck, Jr., J. R. Morris, and M. D. Feit, "Time-dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129–160 (1976).

Steinberg, R. A.

Warner, J.

Wolf, E.

See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1970), pp. 665–681.

Appl. Opt. (2)

Appl. Phys. (1)

The treatment of the paraxial propagation of high-energy laser beams in the atmosphere and other references can be found in J. A. Fleck, Jr., J. R. Morris, and M. D. Feit, "Time-dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129–160 (1976).

IEEE J. Quantum Electron. (2)

A review of such devices can be found in R. C. Alferness, "Guided-wave devices for optical communication," IEEE J. Quantum Electron. QE-17, 946–991 (1981).

D. Marcuse, "Modes of a symmetric slab optical waveguide in birefringent media-Part I: optical axis not in plane of slab," IEEE J. Quantum Electron. QE-14, 736–741 (1978).

J. Opt. Soc. Am. (3)

Other (3)

See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1970), pp. 665–681.

For a comprehensive treatment of the propagation of Gaussian beams, see, for example, J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976), Chap. 2.

This result could be anticipated from the conventional treatment of birefringence. See, for example, Ref. 1. However, the fact that the offset is automatically incorporated in the paraxial wave equation gives assurance that it is correct.

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